PSI - Issue 43

Arnab Bhattacharyya et al. / Procedia Structural Integrity 43 (2023) 35–40 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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The estimated values of J versus the corresponding crack extension,  a for 304LN and SA333 steels are shown in Fig.3. Attempts were made to evaluate the magnitude of the provisional fracture toughness, J Q by locating the intercept of a theoretical blunting line, J = m  o  a, with the J-R curve considering m=2. However, the theoretical blunting line does not intersect the experimental J-R curves. Next an experimental blunting line was constructed and its intersection with the curve J = C 1 (  a ) C 2 in which C 1 and C 2 are material constants, was considered as the J Q value. The estimated J Q values are next examined for the validity of referring these as J C / J IC as per ASTM standard E 1820, which failed. Hence the evaluated J Q values for the materials are denoted as J QC in further discussion. The average estimated fracture toughness of 304LN and SA333 steels are determined as 434 and 364 MPa.m 1/2 respectively. The J-integral fracture toughness values of the other steels are considered from reported literature

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AISI 304LN SS AISI 316LN SS 0.14% C steel SA333 Steel IF steel

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Engineering Strain, % Fig.2. Typical engineering stress-strain plots for the investigated steels: AISI 304LN SS ( ), AISI 316LN SS ( ), 0.14% C steel ( ), SA333 Gr.6 steel ( ) and IF steel ( ). Fracture Toughness from Ball Indentation test: The estimation of FT from ball indentation test (BIT) requires three distinct stages of analysis: (i) understanding indentation load-depth curve and the indentation impression, (ii) stress triaxiality associated with ball indentation deformation and (iii) modified indentation energy to fracture (IEF).Typical variations of indentation load ( P ) with indentation depth ( h t ) for the investigated steels are shown in Fig.4. The plots in Fig.4 can be considered linear only after a certain extent of indentation depth. There are three stages in the development of the plastic zone (PZ) around an indentation: (i) nucleation (ii) development until it envelops the whole indentation, and finally (iii) growth (Haggag et. al., 1989; Murty et al., 1998). At the initial stage of loading, rapid changes of the shape of PZ beneath an indentation is responsible for the non-linear P-h t curves. The non-linear and linear parts of a P-h t curve can thus be attributed to the (Stage I + Stage II) and Stage III development of the PZ around an indentation.

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Fig.3. J-R curve of (a) AISI 304LN stainless steel, (b) SA333 Gr.6 steel. The approach to estimate FT from BIT considers that IEF determined from a BIT which represents the fracture energy of a material. It is based on the inherent assumption that a condition of imaginary fracture exists when true strain of a material during indentation reaches a critical value, referred henceforth as critical fracture strain, and can be estimated from stress triaxiality concept. The stress triaxiality can be calculated from the indentation loads and flow parameters in BIT as: 2 4 /  (1) The stress triaxiality ( I t ) gradually increases with depth of indentation and saturates at a certain indentation depth when the deformation is in fully plastic range (Byun et al., 2000). The saturated stress triaxiality ( I S t ) can be determined from a plot of I t vs. true strain. It is considered here that saturated stress triaxiality of a material follows a 2 3 I t n P d t K  = −